Kranhold F. Topics in Algebraic Topology 2025

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These are the notes of a lecture course on Topics in Algebraic Topology taught by me in summer 2025 at Karlsruhe Institute of Technology, comprising 21 lectures in total. This course is a continuation of a lecture course on Algebraic When referring to an Topology (as taught in winter 2024·25 by Manuel Krannich), and as such, explicit result from the it assumes familiarity with point-set topology, basic notions of homotopy lecture course on Algebraic Topology, I theory and category theory, chain complexes and singular homology, CW shall mention its complexes and cellular homology, derived functors and homology with corresponding number in a margin note, e.g. coefficients, and the Künneth theorem for homology